Thema 8: Maximum Energy-Constrained Dynamic Flow Problem

We study a natural class of flow problems that occur in the context of wireless networks; the objective is to maximize the flow from a set of sources to one sink node within a given time limit, while satisfying a number of constraints. These restrictions include capacities and transit times for edges; in addition, every node has a bound on the amount of transmission it can perform, due to limited battery energy it carries. (S.P. Fekete, A. Hall, E. Köhler, A. Kröller: The Maximum Energy-Constrained Dynamic Flow Problem) Dieses Thema sollte zudem das folgende paper zur Hilfe nehmen: Ford, L.R., Fulkerson, D.R.: Constructing maximal dynamic ﬂows from static ﬂows

Thema 9: Quickest ﬂows over time

Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Traditionally, flows over time are solved in time-expanded networks that contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time-expanded network. We present several approaches for coping with this difficulty. (Fleischer, L., Skutella, M.: Quickest ﬂows over time. SIAM Journal on Computing 36, 1600–1630 (2007) )

Thema 10: The quickest transshipment problem

A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks; each source has a specified supply and each sink has a specified demand. The problem is to send exactly the right amount of flow out of each source and into each sink in the minimum overall time. Variations of the quickest transshipment problem have been studied extensively; the special case of the problem with a single sink is commonly used to model building evacuation. Similar dynamic network flow problems have numerous other applications; in some of these, the capacities are small integers and it is important to find integral flows. There are no polynomial-time algorithms known for most of these problems.In this paper we give the first polynomial-time algorithm for the quickest transshipment problem. Our algorithm provides an integral optimum flow. Previously, the quickest transshipment problem could only be solved efficiently in the special case of a single source and single sink. (Hoppe, B., Tardos, E.: The quickest transshipment problem. Mathematics of Operations Research 25, 36–62 (2000))

Thema 11: How To Learn An Unknown Environment I: The Rectilinear Case

Betrachtet wird das folgende Problem: We consider the problem faced by a robot that must explore and learn an unknown room with obstacles in it. We seek algorithms that achieve a bounded ratio of the worst-case distance traversed in order to see all visible points of the environment (thus creating a map), divided by the optimum distance needed to verify the map, if we had it in the beginning. The situation is complicated by the fact that the latter off-line problem (the problem of optimally verifying a map) is NP-hard. Algorithmen fuer dieses online Problem, insbesondere fuer den rektilinearen Fall sollen vorgestellt werden. (Xiaotie Deng, Tiko Kameda, Christos Papadimitriou: How To Learn An Unknown Environment I: The Rectilinear Case, Journal of the ACM (JACM) Volume 45 Issue 2, March 1998)